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maxMinor -- Returns a maximal minor of the matrix of full rank.

Description

From a given m x n - Matrix of rank r, maxMinor returns an r x r full rank Matrix. This method uses twice the method maxCol by transposing twice. 
i1 : M=matrix {{1,2,3},{1,2,3},{4,5,6},{4,5,6}}

o1 = | 1 2 3 |
     | 1 2 3 |
     | 4 5 6 |
     | 4 5 6 |

              4       3
o1 : Matrix ZZ  <-- ZZ
 
i2 : maxMinor M

o2 = | 1 2 |
     | 4 5 |

              2       2
o2 : Matrix ZZ  <-- ZZ

NOTE: because of the necessity of rank the base field need to be QQ for doing generic evaluation. If not, one gets the message: expected an affine ring (consider Generic=>true to work over QQ). 
i3 : R=QQ[a..g]

o3 = R

o3 : PolynomialRing
 
i4 : M=matrix {{a,a,b},{c,c,d},{e,e,f},{g,g,g}}

o4 = | a a b |
     | c c d |
     | e e f |
     | g g g |

             4      3
o4 : Matrix R  <-- R
 
i5 : maxMinor M

o5 = | a b |
     | c d |

             2      2
o5 : Matrix R  <-- R

See also

Ways to use maxMinor:

  • maxMinor(Matrix)

For the programmer

The object maxMinor is a method function with options.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/EliminationMatrices.m2:1149:0.